MinT - Best Known (137−49, 137, s)-Nets in Base 3

Best Known (137−49, 137, s)-Nets in Base 3

(137−49, 137, 148)-Net over F₃ — Constructive and digital

Digital (88, 137, 148)-net over F₃, using

5 times m-reduction [i] based on digital (88, 142, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 71, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(137−49, 137, 187)-Net over F₃ — Digital

Digital (88, 137, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−49, 137, 2454)-Net in Base 3 — Upper bound on s

There is no (88, 137, 2455)-net in base 3, because

1 times m-reduction [i] would yield (88, 136, 2455)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 78011 484657 451366 028928 232957 695926 912535 082081 171323 252394 505041 > 3¹³⁶ [i]